Depressed persons have better memory for affectively negative than positive stimuli, a pattern generally not exhibited by non-depressed individuals. The mechanisms underlying this differential memory are not clear. In this study we examined memory for valenced and neutral stimuli in depressed and non-depressed individuals under conditions of relatively unconstrained encoding. We developed a novel task based on the game, Concentration, in which participants tried to match pairs of positive and negative words, and pairs of neutral words, hidden under squares in as few turns as possible. Whereas non-depressed participants selected and turned over positive squares more frequently than they did negative squares, depressed participants selected and turned over positive and negative squares equally often. Depressed participants also matched fewer positive word pairs within the first five minutes of the task than did non-depressed participants, and they exhibited poorer learning of positive words. Depressed and non-depressed participants did not differ in their matching of neutral words. These findings add to a growing literature indicating that depression is characterised by difficulties in the processing of positive stimuli.